UCLA Stats 402
data = read.csv('~/Documents/MAS/402/Project 1/pokemon.csv')
names(data) = c('dex', 'name', 'type1', 'type2', 'total', 'hp', 'attack', 'defense', 'spattack',
'spdefense', 'speed', 'generation', 'legendary')
data$generation = as.factor(data$generation)
types = names(table(data$type1))
data$bug = F
data$dark = F
data$dragon = F
data$electric = F
data$fairy = F
data$fighting = F
data$fire = F
data$flying = F
data$ghost = F
data$grass = F
data$ground = F
data$ice = F
data$normal = F
data$poison = F
data$psychic = F
data$rock = F
data$steel = F
data$water = F
for(j in 1:length(types)){
for(i in 1:dim(data)[1]){
if(data$type1[i] == types[j]){
data[i, 13 + j] = T
}
}
}
for(j in 1:length(types)){
for(i in 1:dim(data)[1]){
if(data$type2[i] == types[j]){
data[i, 13 + j] = T
}
}
}
set.seed(1)
t = sample(1:800, 800)
train = data[t[1:500],]
test = data[t[501:800],]
data = train
hist(data$hp, main = 'Histogram of HP', xlab = 'HP')
boxplot(data$hp, main = 'Boxplot of HP', ylab = 'HP')
qqnorm(data$hp, main = 'Normal Quantile Plot of HP', ylab = 'HP')
hist(data$attack, main = 'Histogram of Attack', xlab = 'Attack')
boxplot(data$attack, main = 'Boxplot of Attack', ylab = 'Attack')
hist(data$spattack, main = 'Histogram of Special Attack', xlab = 'Special Attack')
boxplot(data$spattack, main = 'Boxplot of Special Attack', ylab = 'Special Attack')
hist(data$defense, main = 'Histogram of Defense', xlab = 'Defense')
boxplot(data$defense, main = 'Boxplot of Defense', ylab = 'Defense')
hist(data$spdefense, main = 'Histogram of Special Defense', xlab = 'Special Defense')
boxplot(data$spdefense, main = 'Boxplot of Special Defense', ylab = 'Special Defense')
hist(data$speed, main = 'Histogram of Speed', xlab = 'Speed')
boxplot(data$speed, main = 'Boxplot of Speed', ylab = 'Speed')
table(data$generation)
##
## 1 2 3 4 5 6
## 111 71 104 70 97 47
boxplot(data$hp ~ data$generation, main = 'Boxplot of HP by Generation', ylab = 'HP')
table(data$legendary)
##
## False True
## 460 40
boxplot(data$hp ~ data$legendary, main = 'Boxplot of HP by Legendary', ylab = 'HP')
table(data$type1) + table(data$type2)[2:19]
##
## Bug Dark Dragon Electric Fairy Fighting Fire Flying
## 44 39 33 30 24 36 35 67
## Ghost Grass Ground Ice Normal Poison Psychic Rock
## 24 58 42 29 56 43 52 41
## Steel Water
## 31 85
boxplot(data$hp ~ data$type1, main = 'Boxplot of HP by Type 1', ylab = 'HP')
addmargins(table(data$normal, data$flying))
##
## FALSE TRUE Sum
## FALSE 389 55 444
## TRUE 44 12 56
## Sum 433 67 500
boxplot(data$hp ~ data$normal + data$flying, main = 'Boxplot of HP by Types Normal and Flying', xlab = 'Normal.Flying', ylab = 'HP')
addmargins(table(data$bug, data$flying))
##
## FALSE TRUE Sum
## FALSE 399 57 456
## TRUE 34 10 44
## Sum 433 67 500
boxplot(data$hp ~ data$bug + data$flying, main = 'Boxplot of HP by Types Bug and Flying', xlab = 'Bug.Flying', ylab = 'HP')
library(car)
## Loading required package: carData
plot(data$attack, data$hp, main = 'HP by Attack', xlab = 'Attack', ylab = 'HP')
abline(lm(data$hp ~ data$attack))
outlierTest(lm(data$hp ~ data$attack))
## rstudent unadjusted p-value Bonferonni p
## 444 7.192667 2.3517e-12 1.1759e-09
## 67 4.888954 1.3706e-06 6.8529e-04
plot(lm(data$hp ~ data$attack))
influencePlot(lm(data$hp ~ data$attack))
## StudRes Hat CookD
## 67 4.8889544 0.002234555 0.025588096
## 100 -0.3557489 0.021877294 0.001417816
## 375 2.9977570 0.012686333 0.056824314
## 439 1.0703931 0.018134928 0.010577757
## 444 7.1926672 0.006131516 0.144829153
plot(data$spattack, data$hp, main = 'HP by Special Attack', xlab = 'Special Attack', ylab = 'HP')
abline(lm(data$hp ~ data$spattack))
outlierTest(lm(data$hp ~ data$spattack))
## rstudent unadjusted p-value Bonferonni p
## 444 6.423274 3.1239e-10 1.5620e-07
## 67 4.532189 7.3211e-06 3.6606e-03
plot(lm(data$hp ~ data$spattack))
influencePlot(lm(data$hp ~ data$spattack))
## StudRes Hat CookD
## 67 4.53218929 0.002515252 2.491989e-02
## 264 -0.04011011 0.024490516 2.023558e-05
## 286 -2.06207986 0.022419801 4.844326e-02
## 444 6.42327358 0.005352950 1.027178e-01
plot(data$defense, data$hp, main = 'HP by Defense', xlab = 'Defense', ylab = 'HP')
abline(lm(data$hp ~ data$defense))
outlierTest(lm(data$hp ~ data$defense))
## rstudent unadjusted p-value Bonferonni p
## 444 5.703389 2.0183e-08 1.0091e-05
## 67 4.902329 1.2845e-06 6.4223e-04
## 245 -3.962736 8.4951e-05 4.2475e-02
plot(lm(data$hp ~ data$defense))
influencePlot(lm(data$hp ~ data$defense))
## StudRes Hat CookD
## 67 4.90232942 0.003813691 4.396875e-02
## 245 -3.96273585 0.055969840 4.521595e-01
## 307 0.03981347 0.026969177 2.201115e-05
## 374 -1.97215110 0.026969177 5.358941e-02
## 444 5.70338883 0.002541495 3.897358e-02
plot(data$spdefense, data$hp, main = 'HP by Special Defense', xlab = 'Special Defense', ylab = 'HP')
abline(lm(data$hp ~ data$spdefense))
outlierTest(lm(data$hp ~ data$spdefense))
## rstudent unadjusted p-value Bonferonni p
## 444 5.951822 5.0127e-09 2.5063e-06
## 67 5.175570 3.3037e-07 1.6519e-04
## 245 -4.868550 1.5127e-06 7.5637e-04
plot(lm(data$hp ~ data$spdefense))
influencePlot(lm(data$hp ~ data$spdefense))
## StudRes Hat CookD
## 67 5.1755703 0.003821906 0.0488544869
## 245 -4.8685501 0.066075707 0.8019344895
## 264 0.1041085 0.021937885 0.0001217963
## 444 5.9518224 0.002479468 0.0411792181
plot(data$speed, data$hp, main = 'HP by Speed', xlab = 'Speed', ylab = 'HP')
abline(lm(data$hp ~ data$speed))
outlierTest(lm(data$hp ~ data$speed))
## rstudent unadjusted p-value Bonferonni p
## 444 5.788202 1.2614e-08 6.3069e-06
## 67 4.573129 6.0734e-06 3.0367e-03
plot(lm(data$hp ~ data$speed))
influencePlot(lm(data$hp ~ data$speed))
## StudRes Hat CookD
## 67 4.573129 0.002191251 0.02208076
## 134 -1.555796 0.019011157 0.02338745
## 286 -1.336433 0.019011157 0.01727921
## 333 3.536558 0.012401127 0.07675226
## 444 5.788202 0.005261120 0.08317019
summary(data$hp)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 10.00 50.00 65.00 68.21 80.00 190.00
summary(data$attack)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5.00 55.00 75.00 79.03 100.00 180.00
summary(data$spattack)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 10.00 50.00 70.00 73.95 95.00 180.00
summary(data$defense)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5.00 50.00 70.00 73.66 90.00 230.00
summary(data$spdefense)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 20.00 50.00 70.00 71.69 90.00 230.00
summary(data$speed)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5.00 47.50 66.00 68.63 90.00 150.00
tapply(data$hp, data$generation, mean, na.rm = T)
## 1 2 3 4 5 6
## 63.50450 69.12676 65.99038 75.74286 71.00000 65.87234
tapply(data$hp, data$generation, sd, na.rm = T)
## 1 2 3 4 5 6
## 23.12451 27.80027 24.68382 25.10482 20.86315 18.27640
tapply(data$hp, data$generation, var, na.rm = T)
## 1 2 3 4 5 6
## 534.7432 772.8551 609.2912 630.2518 435.2708 334.0268
tapply(data$hp, data$legendary, mean, na.rm = T)
## False True
## 65.88261 94.97500
tapply(data$hp, data$legendary, sd, na.rm = T)
## False True
## 22.79776 19.36490
tapply(data$hp, data$legendary, var, na.rm = T)
## False True
## 519.7378 374.9994
tapply(data$hp, data$type1, mean, na.rm = T)
## Bug Dark Dragon Electric Fairy Fighting Fire Flying
## 58.83721 69.04000 81.70000 61.24000 71.77778 62.09524 70.96429 62.50000
## Ghost Grass Ground Ice Normal Poison Psychic Rock
## 56.75000 65.54545 72.59091 72.73684 73.85185 67.60000 69.39394 62.39286
## Steel Water
## 60.81250 73.34667
tapply(data$hp, data$type1, sd, na.rm = T)
## Bug Dark Dragon Electric Fairy Fighting Fire Flying
## 15.38077 22.15378 23.06079 19.71311 23.16127 19.20392 21.08797 31.81981
## Ghost Grass Ground Ice Normal Poison Psychic Rock
## 29.58265 20.20414 26.76647 21.69189 24.75800 20.09032 33.09073 20.04317
## Steel Water
## 14.37228 27.64079
tapply(data$hp, data$type1, var, na.rm = T)
## Bug Dark Dragon Electric Fairy Fighting Fire
## 236.5681 490.7900 531.8000 388.6067 536.4444 368.7905 444.7024
## Flying Ghost Grass Ground Ice Normal Poison
## 1012.5000 875.1333 408.2072 716.4437 470.5380 612.9588 403.6211
## Psychic Rock Steel Water
## 1094.9962 401.7288 206.5625 764.0133
sort(tapply(data$hp, data$type1, mean, na.rm = T) - mean(data$hp))
## Ghost Bug Steel Electric Fighting Rock
## -11.460000 -9.372791 -7.397500 -6.970000 -6.114762 -5.817143
## Flying Grass Poison Dark Psychic Fire
## -5.710000 -2.664545 -0.610000 0.830000 1.183939 2.754286
## Fairy Ground Ice Water Normal Dragon
## 3.567778 4.380909 4.526842 5.136667 5.641852 13.490000
mfull = lm(hp ~ attack + defense + spattack + spdefense + speed + generation + legendary + bug + dark + dragon + electric + fairy + fighting + fire + flying + ghost + grass + ground + ice + normal + poison + psychic + rock + steel + water + normal*flying + bug*flying, data = data)
summary(mfull)
##
## Call:
## lm(formula = hp ~ attack + defense + spattack + spdefense + speed +
## generation + legendary + bug + dark + dragon + electric +
## fairy + fighting + fire + flying + ghost + grass + ground +
## ice + normal + poison + psychic + rock + steel + water +
## normal * flying + bug * flying, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -47.541 -10.379 -2.351 8.687 139.632
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.03419 4.48587 4.020 6.78e-05 ***
## attack 0.30397 0.03653 8.321 9.64e-16 ***
## defense 0.04940 0.04130 1.196 0.232214
## spattack 0.15012 0.04015 3.739 0.000208 ***
## spdefense 0.15937 0.04136 3.853 0.000133 ***
## speed -0.08563 0.03788 -2.260 0.024251 *
## generation2 8.16726 2.97255 2.748 0.006236 **
## generation3 3.03058 2.65643 1.141 0.254518
## generation4 9.33817 2.95671 3.158 0.001690 **
## generation5 7.65517 2.68488 2.851 0.004548 **
## generation6 6.54225 3.40146 1.923 0.055040 .
## legendaryTrue 2.76070 3.59658 0.768 0.443117
## bugTRUE -2.86478 3.76056 -0.762 0.446565
## darkTRUE -5.73582 3.48824 -1.644 0.100780
## dragonTRUE -0.20348 3.85993 -0.053 0.957982
## electricTRUE -2.78959 4.21222 -0.662 0.508129
## fairyTRUE -0.69349 4.28797 -0.162 0.871588
## fightingTRUE -1.30853 3.77116 -0.347 0.728760
## fireTRUE -4.94841 3.94232 -1.255 0.210031
## flyingTRUE 6.04851 3.17711 1.904 0.057553 .
## ghostTRUE -10.16479 4.31876 -2.354 0.019003 *
## grassTRUE -2.84799 3.18078 -0.895 0.371047
## groundTRUE 5.94677 3.34074 1.780 0.075713 .
## iceTRUE 5.44384 3.94553 1.380 0.168322
## normalTRUE 11.51018 3.77191 3.052 0.002406 **
## poisonTRUE 4.32315 3.50769 1.232 0.218389
## psychicTRUE -0.10211 3.63534 -0.028 0.977604
## rockTRUE -7.92604 3.55214 -2.231 0.026131 *
## steelTRUE -12.45512 4.01574 -3.102 0.002041 **
## waterTRUE 6.04489 2.94185 2.055 0.040454 *
## flyingTRUE:normalTRUE -8.38795 6.69048 -1.254 0.210572
## bugTRUE:flyingTRUE -3.17184 7.41655 -0.428 0.669088
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.2 on 468 degrees of freedom
## Multiple R-squared: 0.455, Adjusted R-squared: 0.4189
## F-statistic: 12.6 on 31 and 468 DF, p-value: < 2.2e-16
outlierTest(mfull)
## rstudent unadjusted p-value Bonferonni p
## 218 8.415041 4.8362e-16 2.4181e-13
## 352 5.626309 3.1774e-08 1.5887e-05
## 545 3.994650 7.5255e-05 3.7627e-02
plot(mfull)
influencePlot(mfull)
## StudRes Hat CookD
## 352 5.626309 0.02845789 0.027194658
## 231 -2.968200 0.21234868 0.073006903
## 138 -1.259418 0.14319834 0.008273783
## 218 8.415041 0.04449261 0.089666656
data[which(t == 231),]
## dex name type1 type2 total hp attack defense spattack spdefense
## 231 213 Shuckle Bug Rock 505 20 10 230 10 230
## speed generation legendary bug dark dragon electric fairy fighting
## 231 5 2 False TRUE FALSE FALSE FALSE FALSE FALSE
## fire flying ghost grass ground ice normal poison psychic rock steel
## 231 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## water
## 231 FALSE
mfull2 = lm(hp ~ attack + defense + spattack + spdefense + speed + generation + legendary + bug + dark + dragon + electric + fairy + fighting + fire + flying + ghost + grass + ground + ice + normal + poison + psychic + rock + steel + water + normal*flying + bug*flying, data = data[-which(t == 231),])
summary(mfull2)
##
## Call:
## lm(formula = hp ~ attack + defense + spattack + spdefense + speed +
## generation + legendary + bug + dark + dragon + electric +
## fairy + fighting + fire + flying + ghost + grass + ground +
## ice + normal + poison + psychic + rock + steel + water +
## normal * flying + bug * flying, data = data[-which(t == 231),
## ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -44.218 -10.322 -2.081 8.288 138.814
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 17.07571 4.46060 3.828 0.000147 ***
## attack 0.28576 0.03675 7.777 4.81e-14 ***
## defense 0.06896 0.04148 1.662 0.097116 .
## spattack 0.13972 0.03997 3.495 0.000519 ***
## spdefense 0.18971 0.04227 4.487 9.09e-06 ***
## speed -0.08951 0.03759 -2.381 0.017665 *
## generation2 8.71213 2.95376 2.950 0.003343 **
## generation3 3.24680 2.63555 1.232 0.218597
## generation4 9.25717 2.93247 3.157 0.001698 **
## generation5 7.74150 2.66291 2.907 0.003821 **
## generation6 6.49197 3.37347 1.924 0.054909 .
## legendaryTrue 2.53639 3.56774 0.711 0.477486
## bugTRUE -1.36726 3.76353 -0.363 0.716551
## darkTRUE -5.47848 3.46058 -1.583 0.114073
## dragonTRUE -0.20747 3.82812 -0.054 0.956801
## electricTRUE -2.95818 4.17789 -0.708 0.479264
## fairyTRUE -1.39549 4.25920 -0.328 0.743329
## fightingTRUE -1.11493 3.74065 -0.298 0.765792
## fireTRUE -4.97363 3.90984 -1.272 0.203978
## flyingTRUE 5.96651 3.15105 1.893 0.058909 .
## ghostTRUE -10.39395 4.28386 -2.426 0.015631 *
## grassTRUE -3.14884 3.15619 -0.998 0.318955
## groundTRUE 5.79020 3.31363 1.747 0.081227 .
## iceTRUE 5.28003 3.91340 1.349 0.177920
## normalTRUE 11.45817 3.74087 3.063 0.002318 **
## poisonTRUE 3.97272 3.48078 1.141 0.254318
## psychicTRUE -0.69124 3.61084 -0.191 0.848268
## rockTRUE -7.36291 3.52797 -2.087 0.037429 *
## steelTRUE -13.80663 4.00859 -3.444 0.000624 ***
## waterTRUE 5.73735 2.91944 1.965 0.049981 *
## flyingTRUE:normalTRUE -7.84262 6.63788 -1.181 0.238008
## bugTRUE:flyingTRUE -4.82948 7.37660 -0.655 0.512981
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.05 on 467 degrees of freedom
## Multiple R-squared: 0.4606, Adjusted R-squared: 0.4248
## F-statistic: 12.87 on 31 and 467 DF, p-value: < 2.2e-16
outlierTest(mfull2)
## rstudent unadjusted p-value Bonferonni p
## 218 8.440826 4.0144e-16 2.0032e-13
## 352 5.779844 1.3702e-08 6.8375e-06
## 351 4.023857 6.6798e-05 3.3332e-02
## 545 3.951437 8.9721e-05 4.4771e-02
plot(mfull2)
influencePlot(mfull2)
## StudRes Hat CookD
## 751 -0.6441763 0.14572503 0.002214830
## 352 5.7798435 0.02936398 0.029532708
## 545 3.9514371 0.11128913 0.059247540
## 138 -1.2681354 0.14319864 0.008388317
## 218 8.4408261 0.04472630 0.090614459
library(effects)
## lattice theme set by effectsTheme()
## See ?effectsTheme for details.
data$normal = as.factor(data$normal)
data$bug = as.factor(data$bug)
data$flying = as.factor(data$flying)
plot(allEffects(lm(hp ~ normal*flying + bug*flying, data = data), ask = F))
library(MASS)
maic = stepAIC(mfull2)
## Start: AIC=2918.14
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + dragon + electric + fairy + fighting +
## fire + flying + ghost + grass + ground + ice + normal + poison +
## psychic + rock + steel + water + normal * flying + bug *
## flying
##
## Df Sum of Sq RSS AIC
## - dragon 1 1.0 152105 2916.1
## - psychic 1 11.9 152116 2916.2
## - fighting 1 28.9 152133 2916.2
## - fairy 1 35.0 152139 2916.2
## - bug:flying 1 139.6 152244 2916.6
## - electric 1 163.3 152267 2916.7
## - legendary 1 164.6 152269 2916.7
## - grass 1 324.2 152428 2917.2
## - poison 1 424.3 152528 2917.5
## - flying:normal 1 454.7 152559 2917.6
## - fire 1 527.1 152631 2917.9
## - ice 1 592.9 152697 2918.1
## <none> 152104 2918.1
## - dark 1 816.3 152920 2918.8
## - defense 1 900.0 153004 2919.1
## - ground 1 994.5 153098 2919.4
## - water 1 1257.9 153362 2920.2
## - rock 1 1418.6 153523 2920.8
## - speed 1 1846.5 153950 2922.2
## - ghost 1 1917.4 154021 2922.4
## - generation 5 5308.2 157412 2925.2
## - steel 1 3863.8 155968 2928.7
## - spattack 1 3979.1 156083 2929.0
## - spdefense 1 6558.8 158663 2937.2
## - attack 1 19697.1 171801 2976.9
##
## Step: AIC=2916.14
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + electric + fairy + fighting + fire +
## flying + ghost + grass + ground + ice + normal + poison +
## psychic + rock + steel + water + flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - psychic 1 11.0 152116 2914.2
## - fighting 1 28.2 152133 2914.2
## - fairy 1 34.0 152139 2914.2
## - bug:flying 1 138.7 152244 2914.6
## - legendary 1 163.9 152269 2914.7
## - electric 1 166.7 152272 2914.7
## - grass 1 348.8 152454 2915.3
## - poison 1 452.0 152557 2915.6
## - flying:normal 1 455.7 152561 2915.6
## - fire 1 559.2 152664 2916.0
## <none> 152105 2916.1
## - ice 1 632.4 152737 2916.2
## - dark 1 850.2 152955 2916.9
## - defense 1 899.3 153004 2917.1
## - ground 1 1028.7 153134 2917.5
## - water 1 1444.0 153549 2918.9
## - rock 1 1469.5 153575 2918.9
## - speed 1 1847.2 153952 2920.2
## - ghost 1 1978.3 154083 2920.6
## - generation 5 5310.0 157415 2923.3
## - steel 1 3987.0 156092 2927.1
## - spattack 1 4013.5 156118 2927.1
## - spdefense 1 6562.2 158667 2935.2
## - attack 1 19756.5 171861 2975.1
##
## Step: AIC=2914.18
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + electric + fairy + fighting + fire +
## flying + ghost + grass + ground + ice + normal + poison +
## rock + steel + water + flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - fighting 1 24.1 152140 2912.3
## - fairy 1 27.8 152144 2912.3
## - bug:flying 1 134.8 152251 2912.6
## - electric 1 158.4 152274 2912.7
## - legendary 1 163.4 152279 2912.7
## - grass 1 350.2 152466 2913.3
## - flying:normal 1 461.8 152578 2913.7
## - poison 1 527.9 152644 2913.9
## - fire 1 573.3 152689 2914.1
## <none> 152116 2914.2
## - ice 1 720.4 152836 2914.5
## - dark 1 843.7 152960 2914.9
## - defense 1 895.9 153012 2915.1
## - ground 1 1081.8 153198 2915.7
## - rock 1 1465.8 153582 2917.0
## - water 1 1827.8 153944 2918.1
## - speed 1 1871.5 153987 2918.3
## - ghost 1 2015.5 154131 2918.7
## - generation 5 5345.2 157461 2921.4
## - steel 1 3985.8 156102 2925.1
## - spattack 1 4201.2 156317 2925.8
## - spdefense 1 6585.5 158701 2933.3
## - attack 1 22128.1 174244 2979.9
##
## Step: AIC=2912.26
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + electric + fairy + fire + flying +
## ghost + grass + ground + ice + normal + poison + rock + steel +
## water + flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - fairy 1 21.9 152162 2910.3
## - bug:flying 1 142.3 152282 2910.7
## - electric 1 143.7 152284 2910.7
## - legendary 1 172.3 152312 2910.8
## - grass 1 330.9 152471 2911.3
## - flying:normal 1 476.6 152617 2911.8
## - fire 1 560.4 152700 2912.1
## - poison 1 563.0 152703 2912.1
## <none> 152140 2912.3
## - ice 1 797.1 152937 2912.9
## - dark 1 819.8 152960 2912.9
## - defense 1 910.5 153051 2913.2
## - ground 1 1224.6 153365 2914.3
## - rock 1 1442.4 153582 2915.0
## - speed 1 1894.9 154035 2916.4
## - water 1 1985.0 154125 2916.7
## - ghost 1 1992.3 154132 2916.8
## - generation 5 5323.6 157464 2919.4
## - steel 1 3965.3 156105 2923.1
## - spattack 1 4495.3 156635 2924.8
## - spdefense 1 6562.6 158703 2931.3
## - attack 1 23036.7 175177 2980.6
##
## Step: AIC=2910.33
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + electric + fire + flying + ghost +
## grass + ground + ice + normal + poison + rock + steel + water +
## flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - electric 1 130.3 152292 2908.8
## - bug:flying 1 140.7 152303 2908.8
## - legendary 1 175.9 152338 2908.9
## - grass 1 315.0 152477 2909.4
## - flying:normal 1 478.6 152641 2909.9
## - fire 1 539.9 152702 2910.1
## - poison 1 597.3 152759 2910.3
## <none> 152162 2910.3
## - dark 1 801.4 152963 2910.9
## - ice 1 840.9 153003 2911.1
## - defense 1 914.9 153077 2911.3
## - ground 1 1266.6 153429 2912.5
## - rock 1 1422.8 153585 2913.0
## - speed 1 1874.5 154036 2914.4
## - ghost 1 1972.3 154134 2914.8
## - water 1 2105.4 154267 2915.2
## - generation 5 5312.4 157474 2917.4
## - steel 1 3970.4 156132 2921.2
## - spattack 1 4475.6 156637 2922.8
## - spdefense 1 6550.6 158713 2929.4
## - attack 1 23547.5 175709 2980.1
##
## Step: AIC=2908.75
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + fire + flying + ghost + grass +
## ground + ice + normal + poison + rock + steel + water + flying:normal +
## bug:flying
##
## Df Sum of Sq RSS AIC
## - bug:flying 1 124.9 152417 2907.2
## - legendary 1 183.2 152475 2907.3
## - grass 1 266.2 152558 2907.6
## - fire 1 469.3 152762 2908.3
## - flying:normal 1 478.2 152770 2908.3
## <none> 152292 2908.8
## - poison 1 692.6 152985 2909.0
## - dark 1 737.3 153030 2909.2
## - defense 1 910.3 153203 2909.7
## - ice 1 946.5 153239 2909.8
## - ground 1 1316.4 153609 2911.1
## - rock 1 1362.9 153655 2911.2
## - ghost 1 1895.0 154187 2912.9
## - speed 1 1930.3 154223 2913.0
## - water 1 2403.3 154696 2914.6
## - generation 5 5242.9 157535 2915.6
## - steel 1 3961.7 156254 2919.6
## - spattack 1 4345.7 156638 2920.8
## - spdefense 1 6674.5 158967 2928.2
## - attack 1 24220.6 176513 2980.4
##
## Step: AIC=2907.16
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + fire + flying + ghost + grass +
## ground + ice + normal + poison + rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - bug 1 114.7 152532 2905.5
## - legendary 1 223.1 152640 2905.9
## - grass 1 251.9 152669 2906.0
## - flying:normal 1 409.1 152826 2906.5
## - fire 1 446.5 152864 2906.6
## <none> 152417 2907.2
## - dark 1 731.8 153149 2907.6
## - poison 1 766.2 153183 2907.7
## - defense 1 919.2 153336 2908.2
## - ice 1 954.0 153371 2908.3
## - ground 1 1312.3 153729 2909.4
## - rock 1 1345.2 153762 2909.6
## - speed 1 1876.1 154293 2911.3
## - ghost 1 1909.2 154326 2911.4
## - water 1 2414.3 154831 2913.0
## - generation 5 5206.4 157624 2913.9
## - steel 1 3876.8 156294 2917.7
## - spattack 1 4232.3 156649 2918.8
## - spdefense 1 6652.4 159070 2926.5
## - attack 1 24235.4 176653 2978.8
##
## Step: AIC=2905.54
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + dark + fire + flying + ghost + grass + ground +
## ice + normal + poison + rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - grass 1 221.9 152754 2904.3
## - legendary 1 240.7 152773 2904.3
## - flying:normal 1 391.0 152923 2904.8
## - fire 1 406.4 152938 2904.9
## <none> 152532 2905.5
## - dark 1 672.2 153204 2905.7
## - poison 1 725.8 153258 2905.9
## - defense 1 891.1 153423 2906.4
## - ice 1 1029.5 153561 2906.9
## - rock 1 1296.7 153829 2907.8
## - ground 1 1431.1 153963 2908.2
## - ghost 1 1832.9 154365 2909.5
## - speed 1 1887.1 154419 2909.7
## - generation 5 5136.8 157669 2912.1
## - water 1 2701.4 155233 2912.3
## - steel 1 3888.0 156420 2916.1
## - spattack 1 4418.3 156950 2917.8
## - spdefense 1 6805.6 159337 2925.3
## - attack 1 24180.4 176712 2977.0
##
## Step: AIC=2904.26
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + dark + fire + flying + ghost + ground + ice +
## normal + poison + rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - legendary 1 257.9 153012 2903.1
## - fire 1 330.6 153084 2903.3
## - flying:normal 1 407.6 153161 2903.6
## - dark 1 605.0 153359 2904.2
## <none> 152754 2904.3
## - poison 1 711.6 153465 2904.6
## - defense 1 861.4 153615 2905.1
## - ice 1 1122.5 153876 2905.9
## - rock 1 1196.7 153950 2906.2
## - ground 1 1603.6 154357 2907.5
## - ghost 1 1763.9 154518 2908.0
## - speed 1 1771.5 154525 2908.0
## - generation 5 5031.1 157785 2910.4
## - water 1 3099.0 155853 2912.3
## - steel 1 3685.6 156439 2914.2
## - spattack 1 4314.6 157068 2916.2
## - spdefense 1 6842.5 159596 2924.1
## - attack 1 24252.2 177006 2975.8
##
## Step: AIC=2903.11
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## dark + fire + flying + ghost + ground + ice + normal + poison +
## rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - fire 1 338.5 153350 2902.2
## - flying:normal 1 446.3 153458 2902.6
## <none> 153012 2903.1
## - dark 1 671.8 153683 2903.3
## - poison 1 684.8 153696 2903.3
## - defense 1 924.9 153936 2904.1
## - ice 1 1095.1 154107 2904.7
## - rock 1 1227.8 154239 2905.1
## - ground 1 1652.9 154665 2906.5
## - speed 1 1692.6 154704 2906.6
## - ghost 1 1783.1 154795 2906.9
## - generation 5 5275.1 158287 2910.0
## - water 1 2996.0 156008 2910.8
## - steel 1 3890.2 156902 2913.6
## - spattack 1 4958.4 157970 2917.0
## - spdefense 1 7206.7 160218 2924.1
## - attack 1 25589.4 178601 2978.3
##
## Step: AIC=2902.21
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## dark + flying + ghost + ground + ice + normal + poison +
## rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - flying:normal 1 448.4 153798 2901.7
## <none> 153350 2902.2
## - dark 1 642.1 153992 2902.3
## - poison 1 800.4 154150 2902.8
## - defense 1 916.7 154267 2903.2
## - rock 1 1185.6 154536 2904.1
## - ice 1 1248.2 154598 2904.2
## - ground 1 1682.2 155032 2905.7
## - speed 1 1706.1 155056 2905.7
## - ghost 1 1756.0 155106 2905.9
## - generation 5 5142.5 158493 2908.7
## - water 1 3378.8 156729 2911.1
## - steel 1 3746.3 157096 2912.2
## - spattack 1 4638.0 157988 2915.1
## - spdefense 1 7489.9 160840 2924.0
## - attack 1 25566.6 178917 2977.2
##
## Step: AIC=2901.67
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## dark + flying + ghost + ground + ice + normal + poison +
## rock + steel + water
##
## Df Sum of Sq RSS AIC
## <none> 153798 2901.7
## - dark 1 669.4 154468 2901.8
## - poison 1 785.7 154584 2902.2
## - defense 1 915.2 154714 2902.6
## - flying 1 1197.9 154996 2903.5
## - ice 1 1199.8 154998 2903.5
## - rock 1 1209.9 155008 2903.6
## - ground 1 1656.5 155455 2905.0
## - speed 1 1666.3 155465 2905.0
## - ghost 1 1801.8 155600 2905.5
## - generation 5 5387.2 159186 2908.8
## - water 1 3307.3 157106 2910.3
## - steel 1 3881.2 157680 2912.1
## - spattack 1 4544.1 158343 2914.2
## - normal 1 5657.6 159456 2917.7
## - spdefense 1 7753.7 161552 2924.2
## - attack 1 25630.8 179429 2976.6
summary(maic)
##
## Call:
## lm(formula = hp ~ attack + defense + spattack + spdefense + speed +
## generation + dark + flying + ghost + ground + ice + normal +
## poison + rock + steel + water, data = data[-which(t == 231),
## ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.650 -10.614 -2.575 8.437 140.565
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.97162 3.75668 3.719 0.000224 ***
## attack 0.29368 0.03291 8.925 < 2e-16 ***
## defense 0.06911 0.04098 1.687 0.092350 .
## spattack 0.13027 0.03467 3.758 0.000192 ***
## spdefense 0.20067 0.04088 4.909 1.26e-06 ***
## speed -0.08354 0.03671 -2.276 0.023306 *
## generation2 8.58241 2.89323 2.966 0.003164 **
## generation3 3.37154 2.57415 1.310 0.190902
## generation4 9.24855 2.86732 3.226 0.001344 **
## generation5 7.80147 2.61605 2.982 0.003008 **
## generation6 6.37553 3.28490 1.941 0.052863 .
## darkTRUE -4.52930 3.14007 -1.442 0.149839
## flyingTRUE 4.78515 2.48000 1.929 0.054261 .
## ghostTRUE -9.33299 3.94397 -2.366 0.018360 *
## groundTRUE 6.94635 3.06142 2.269 0.023713 *
## iceTRUE 6.76176 3.50160 1.931 0.054068 .
## normalTRUE 11.65337 2.77907 4.193 3.28e-05 ***
## poisonTRUE 4.90115 3.13649 1.563 0.118803
## rockTRUE -6.38275 3.29147 -1.939 0.053068 .
## steelTRUE -13.09680 3.77089 -3.473 0.000561 ***
## waterTRUE 7.29443 2.27519 3.206 0.001436 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17.94 on 478 degrees of freedom
## Multiple R-squared: 0.4546, Adjusted R-squared: 0.4318
## F-statistic: 19.92 on 20 and 478 DF, p-value: < 2.2e-16
outlierTest(maic)
## rstudent unadjusted p-value Bonferonni p
## 218 8.497498 2.4930e-16 1.2440e-13
## 352 5.847534 9.2669e-09 4.6242e-06
## 351 4.089665 5.0703e-05 2.5301e-02
## 545 4.035555 6.3439e-05 3.1656e-02
plot(maic)
influencePlot(maic)
## StudRes Hat CookD
## 751 -0.5999364 0.13983316 0.002789976
## 352 5.8475342 0.02641985 0.041316865
## 545 4.0355547 0.06609091 0.053180657
## 99 -1.9434648 0.11917870 0.024195192
## 218 8.4974983 0.02285907 0.070009304
vif(maic)
## GVIF Df GVIF^(1/(2*Df))
## attack 1.709810 1 1.307597
## defense 2.235812 1 1.495263
## spattack 1.852368 1 1.361017
## spdefense 1.900783 1 1.378689
## speed 1.613357 1 1.270180
## generation 1.369209 5 1.031922
## dark 1.101732 1 1.049634
## flying 1.108758 1 1.052976
## ghost 1.104451 1 1.050929
## ground 1.120436 1 1.058506
## ice 1.040890 1 1.020240
## normal 1.193344 1 1.092403
## poison 1.201426 1 1.096096
## rock 1.238878 1 1.113049
## steel 1.284905 1 1.133537
## water 1.134571 1 1.065162
mbic = stepAIC(mfull2, k = log(length(mfull2$residuals)))
## Start: AIC=3052.94
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + dragon + electric + fairy + fighting +
## fire + flying + ghost + grass + ground + ice + normal + poison +
## psychic + rock + steel + water + normal * flying + bug *
## flying
##
## Df Sum of Sq RSS AIC
## - generation 5 5308.2 157412 3039.0
## - dragon 1 1.0 152105 3046.7
## - psychic 1 11.9 152116 3046.8
## - fighting 1 28.9 152133 3046.8
## - fairy 1 35.0 152139 3046.8
## - bug:flying 1 139.6 152244 3047.2
## - electric 1 163.3 152267 3047.3
## - legendary 1 164.6 152269 3047.3
## - grass 1 324.2 152428 3047.8
## - poison 1 424.3 152528 3048.1
## - flying:normal 1 454.7 152559 3048.2
## - fire 1 527.1 152631 3048.4
## - ice 1 592.9 152697 3048.7
## - dark 1 816.3 152920 3049.4
## - defense 1 900.0 153004 3049.7
## - ground 1 994.5 153098 3050.0
## - water 1 1257.9 153362 3050.8
## - rock 1 1418.6 153523 3051.4
## - speed 1 1846.5 153950 3052.8
## <none> 152104 3052.9
## - ghost 1 1917.4 154021 3053.0
## - steel 1 3863.8 155968 3059.2
## - spattack 1 3979.1 156083 3059.6
## - spdefense 1 6558.8 158663 3067.8
## - attack 1 19697.1 171801 3107.5
##
## Step: AIC=3038.99
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## bug + dark + dragon + electric + fairy + fighting + fire +
## flying + ghost + grass + ground + ice + normal + poison +
## psychic + rock + steel + water + flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - dragon 1 2.8 157415 3032.8
## - fighting 1 4.0 157416 3032.8
## - fairy 1 19.1 157431 3032.8
## - psychic 1 36.2 157448 3032.9
## - poison 1 53.6 157466 3032.9
## - electric 1 92.3 157504 3033.1
## - bug:flying 1 101.4 157514 3033.1
## - grass 1 180.6 157593 3033.3
## - fire 1 322.8 157735 3033.8
## - dark 1 400.2 157812 3034.1
## - legendary 1 404.8 157817 3034.1
## - flying:normal 1 669.8 158082 3034.9
## - defense 1 679.1 158091 3034.9
## - ice 1 939.9 158352 3035.8
## - water 1 993.4 158406 3035.9
## - ground 1 1069.9 158482 3036.2
## - rock 1 1312.3 158725 3036.9
## - ghost 1 1927.9 159340 3038.9
## <none> 157412 3039.0
## - speed 1 2290.4 159703 3040.0
## - steel 1 3076.3 160489 3042.4
## - spattack 1 3824.2 161236 3044.8
## - spdefense 1 7647.5 165060 3056.4
## - attack 1 19283.7 176696 3090.4
##
## Step: AIC=3032.79
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## bug + dark + electric + fairy + fighting + fire + flying +
## ghost + grass + ground + ice + normal + poison + psychic +
## rock + steel + water + flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - fighting 1 6.4 157421 3026.6
## - fairy 1 22.2 157437 3026.7
## - psychic 1 46.2 157461 3026.7
## - poison 1 50.9 157466 3026.7
## - bug:flying 1 103.6 157519 3026.9
## - electric 1 106.2 157521 3026.9
## - grass 1 214.7 157630 3027.3
## - fire 1 370.1 157785 3027.8
## - legendary 1 408.5 157823 3027.9
## - dark 1 437.4 157852 3028.0
## - flying:normal 1 668.5 158083 3028.7
## - defense 1 683.7 158099 3028.7
## - ice 1 962.0 158377 3029.6
## - ground 1 1078.5 158494 3030.0
## - water 1 1081.1 158496 3030.0
## - rock 1 1397.8 158813 3031.0
## <none> 157415 3032.8
## - ghost 1 2018.9 159434 3032.9
## - speed 1 2290.0 159705 3033.8
## - steel 1 3217.8 160633 3036.7
## - spattack 1 3891.2 161306 3038.8
## - spdefense 1 7665.6 165081 3050.3
## - attack 1 19407.1 176822 3084.6
##
## Step: AIC=3026.6
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## bug + dark + electric + fairy + fire + flying + ghost + grass +
## ground + ice + normal + poison + psychic + rock + steel +
## water + flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - fairy 1 19.0 157440 3020.4
## - psychic 1 42.3 157464 3020.5
## - poison 1 58.3 157480 3020.6
## - electric 1 100.2 157522 3020.7
## - bug:flying 1 106.3 157528 3020.7
## - grass 1 208.4 157630 3021.1
## - fire 1 363.8 157785 3021.5
## - legendary 1 416.3 157838 3021.7
## - dark 1 434.1 157856 3021.8
## - flying:normal 1 680.4 158102 3022.5
## - defense 1 690.0 158111 3022.6
## - ice 1 1041.1 158462 3023.7
## - water 1 1188.6 158610 3024.1
## - ground 1 1195.6 158617 3024.2
## - rock 1 1405.9 158827 3024.8
## <none> 157421 3026.6
## - ghost 1 2036.4 159458 3026.8
## - speed 1 2312.5 159734 3027.7
## - steel 1 3231.7 160653 3030.5
## - spattack 1 4026.3 161448 3033.0
## - spdefense 1 7665.6 165087 3044.1
## - attack 1 19940.8 177362 3079.9
##
## Step: AIC=3020.45
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## bug + dark + electric + fire + flying + ghost + grass + ground +
## ice + normal + poison + psychic + rock + steel + water +
## flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - psychic 1 34.0 157474 3014.3
## - poison 1 73.0 157513 3014.5
## - electric 1 86.8 157527 3014.5
## - bug:flying 1 104.2 157545 3014.6
## - grass 1 192.9 157633 3014.8
## - fire 1 345.5 157786 3015.3
## - dark 1 418.6 157859 3015.6
## - legendary 1 420.4 157861 3015.6
## - flying:normal 1 682.7 158123 3016.4
## - defense 1 694.0 158134 3016.4
## - ice 1 1112.4 158553 3017.8
## - ground 1 1246.4 158687 3018.2
## - water 1 1311.6 158752 3018.4
## - rock 1 1387.2 158827 3018.6
## <none> 157440 3020.4
## - ghost 1 2025.2 159466 3020.6
## - speed 1 2293.9 159734 3021.4
## - steel 1 3230.3 160671 3024.4
## - spattack 1 4009.4 161450 3026.8
## - spdefense 1 7686.1 165126 3038.0
## - attack 1 20815.5 178256 3076.2
##
## Step: AIC=3014.34
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## bug + dark + electric + fire + flying + ghost + grass + ground +
## ice + normal + poison + rock + steel + water + flying:normal +
## bug:flying
##
## Df Sum of Sq RSS AIC
## - electric 1 60.8 157535 3008.3
## - bug:flying 1 97.5 157572 3008.4
## - poison 1 105.4 157580 3008.5
## - grass 1 161.2 157636 3008.6
## - fire 1 311.5 157786 3009.1
## - dark 1 392.9 157867 3009.4
## - legendary 1 416.7 157891 3009.4
## - defense 1 687.0 158161 3010.3
## - flying:normal 1 691.9 158166 3010.3
## - ice 1 1254.7 158729 3012.1
## - ground 1 1296.8 158771 3012.2
## - rock 1 1354.9 158829 3012.4
## - water 1 1662.6 159137 3013.4
## <none> 157474 3014.3
## - ghost 1 1997.5 159472 3014.4
## - speed 1 2338.2 159813 3015.5
## - steel 1 3196.9 160671 3018.2
## - spattack 1 4134.6 161609 3021.1
## - spdefense 1 7654.8 165129 3031.8
## - attack 1 23773.0 181247 3078.3
##
## Step: AIC=3008.32
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## bug + dark + fire + flying + ghost + grass + ground + ice +
## normal + poison + rock + steel + water + flying:normal +
## bug:flying
##
## Df Sum of Sq RSS AIC
## - bug:flying 1 88.4 157624 3002.4
## - poison 1 131.7 157667 3002.5
## - grass 1 136.7 157672 3002.5
## - fire 1 276.6 157812 3003.0
## - dark 1 362.6 157898 3003.3
## - legendary 1 424.2 157959 3003.4
## - defense 1 684.1 158219 3004.3
## - flying:normal 1 690.2 158225 3004.3
## - rock 1 1317.2 158852 3006.3
## - ground 1 1333.0 158868 3006.3
## - ice 1 1345.7 158881 3006.3
## - water 1 1860.9 159396 3008.0
## - ghost 1 1945.1 159480 3008.2
## <none> 157535 3008.3
## - speed 1 2383.1 159918 3009.6
## - steel 1 3191.3 160726 3012.1
## - spattack 1 4087.4 161623 3014.9
## - spdefense 1 7741.9 165277 3026.1
## - attack 1 24352.3 181887 3073.8
##
## Step: AIC=3002.39
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## bug + dark + fire + flying + ghost + grass + ground + ice +
## normal + poison + rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - bug 1 45.1 157669 2996.3
## - grass 1 129.2 157753 2996.6
## - poison 1 160.7 157784 2996.7
## - fire 1 262.5 157886 2997.0
## - dark 1 359.7 157983 2997.3
## - legendary 1 473.8 158097 2997.7
## - flying:normal 1 624.4 158248 2998.2
## - defense 1 692.2 158316 2998.4
## - rock 1 1302.8 158926 3000.3
## - ground 1 1325.2 158949 3000.3
## - ice 1 1350.8 158974 3000.4
## - water 1 1867.9 159491 3002.1
## - ghost 1 1961.8 159585 3002.3
## <none> 157624 3002.4
## - speed 1 2330.0 159954 3003.5
## - steel 1 3136.6 160760 3006.0
## - spattack 1 4001.0 161625 3008.7
## - spdefense 1 7707.3 165331 3020.0
## - attack 1 24391.6 182015 3068.0
##
## Step: AIC=2996.32
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## dark + fire + flying + ghost + grass + ground + ice + normal +
## poison + rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - grass 1 116.2 157785 2990.5
## - poison 1 150.0 157819 2990.6
## - fire 1 243.7 157912 2990.9
## - dark 1 334.9 158004 2991.2
## - legendary 1 489.0 158158 2991.7
## - flying:normal 1 610.0 158279 2992.0
## - defense 1 678.1 158347 2992.2
## - rock 1 1274.9 158944 2994.1
## - ground 1 1407.0 159076 2994.5
## - ice 1 1409.7 159078 2994.6
## - ghost 1 1920.3 159589 2996.2
## <none> 157669 2996.3
## - water 1 2052.5 159721 2996.6
## - speed 1 2335.7 160004 2997.4
## - steel 1 3147.0 160816 3000.0
## - spattack 1 4131.0 161800 3003.0
## - spdefense 1 7821.2 165490 3014.3
## - attack 1 24359.0 182028 3061.8
##
## Step: AIC=2990.47
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## dark + fire + flying + ghost + ground + ice + normal + poison +
## rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - poison 1 152.2 157937 2984.7
## - fire 1 199.8 157985 2984.9
## - dark 1 303.0 158088 2985.2
## - legendary 1 501.9 158287 2985.8
## - flying:normal 1 623.5 158408 2986.2
## - defense 1 661.9 158447 2986.3
## - rock 1 1207.2 158992 2988.1
## - ice 1 1489.8 159275 2988.9
## - ground 1 1535.1 159320 2989.1
## - ghost 1 1880.7 159666 2990.2
## <none> 157785 2990.5
## - speed 1 2247.9 160033 2991.3
## - water 1 2333.8 160119 2991.6
## - steel 1 3034.3 160819 2993.8
## - spattack 1 4059.2 161844 2996.9
## - spdefense 1 7848.4 165633 3008.5
## - attack 1 24401.7 182186 3056.0
##
## Step: AIC=2984.74
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## dark + fire + flying + ghost + ground + ice + normal + rock +
## steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - fire 1 246.5 158183 2979.3
## - dark 1 351.6 158289 2979.6
## - legendary 1 471.6 158409 2980.0
## - flying:normal 1 607.0 158544 2980.4
## - defense 1 653.2 158590 2980.6
## - rock 1 1306.3 159243 2982.6
## - ice 1 1400.1 159337 2982.9
## - ground 1 1455.7 159393 2983.1
## - ghost 1 1880.5 159818 2984.4
## <none> 157937 2984.7
## - water 1 2212.0 160149 2985.5
## - speed 1 2257.2 160194 2985.6
## - steel 1 3234.9 161172 2988.7
## - spattack 1 4024.6 161962 2991.1
## - spdefense 1 7839.6 165777 3002.7
## - attack 1 24394.6 182332 3050.2
##
## Step: AIC=2979.31
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## dark + flying + ghost + ground + ice + normal + rock + steel +
## water + flying:normal
##
## Df Sum of Sq RSS AIC
## - dark 1 339.9 158523 2974.2
## - legendary 1 473.4 158657 2974.6
## - flying:normal 1 598.3 158782 2975.0
## - defense 1 649.2 158833 2975.1
## - rock 1 1284.5 159468 2977.1
## - ground 1 1472.0 159656 2977.7
## - ice 1 1525.8 159709 2977.9
## - ghost 1 1856.0 160040 2978.9
## <none> 158183 2979.3
## - speed 1 2260.4 160444 2980.2
## - water 1 2470.4 160654 2980.8
## - steel 1 3145.3 161329 2982.9
## - spattack 1 3788.7 161972 2984.9
## - spdefense 1 8024.6 166208 2997.8
## - attack 1 24443.3 182627 3044.8
##
## Step: AIC=2974.17
## hp ~ attack + defense + spattack + spdefense + speed + legendary +
## flying + ghost + ground + ice + normal + rock + steel + water +
## flying:normal
##
## Df Sum of Sq RSS AIC
## - legendary 1 528.7 159052 2969.6
## - flying:normal 1 607.6 159131 2969.9
## - defense 1 707.0 159230 2970.2
## - rock 1 1216.9 159740 2971.8
## - ground 1 1536.2 160060 2972.8
## - ice 1 1582.5 160106 2972.9
## - ghost 1 1916.8 160440 2973.9
## <none> 158523 2974.2
## - speed 1 2319.5 160843 2975.2
## - water 1 2556.0 161079 2975.9
## - steel 1 3039.4 161563 2977.4
## - spattack 1 3865.2 162389 2980.0
## - spdefense 1 8020.9 166544 2992.6
## - attack 1 24282.5 182806 3039.1
##
## Step: AIC=2969.62
## hp ~ attack + defense + spattack + spdefense + speed + flying +
## ghost + ground + ice + normal + rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - flying:normal 1 687.0 159739 2965.6
## - defense 1 788.5 159841 2965.9
## - rock 1 1245.1 160297 2967.3
## - ice 1 1561.1 160613 2968.3
## - ground 1 1621.3 160673 2968.5
## - ghost 1 1934.6 160987 2969.4
## <none> 159052 2969.6
## - speed 1 2203.3 161255 2970.3
## - water 1 2413.0 161465 2970.9
## - steel 1 3229.3 162281 2973.4
## - spattack 1 4711.3 163763 2978.0
## - spdefense 1 8620.8 167673 2989.7
## - attack 1 25813.1 184865 3038.4
##
## Step: AIC=2965.55
## hp ~ attack + defense + spattack + spdefense + speed + flying +
## ghost + ground + ice + normal + rock + steel + water
##
## Df Sum of Sq RSS AIC
## - defense 1 780.1 160519 2961.8
## - rock 1 1270.7 161010 2963.3
## - flying 1 1378.1 161117 2963.6
## - ice 1 1509.4 161248 2964.0
## - ground 1 1601.0 161340 2964.3
## <none> 159739 2965.6
## - ghost 1 2001.3 161740 2965.6
## - speed 1 2172.9 161912 2966.1
## - water 1 2329.8 162069 2966.6
## - steel 1 3341.9 163081 2969.7
## - spattack 1 4605.5 164345 2973.5
## - normal 1 6212.1 165951 2978.4
## - spdefense 1 9049.1 168788 2986.8
## - attack 1 25824.6 185564 3034.1
##
## Step: AIC=2961.77
## hp ~ attack + spattack + spdefense + speed + flying + ghost +
## ground + ice + normal + rock + steel + water
##
## Df Sum of Sq RSS AIC
## - rock 1 806 161325 2958.1
## - flying 1 1405 161924 2959.9
## - ice 1 1527 162046 2960.3
## - ghost 1 1817 162336 2961.2
## - ground 1 1835 162354 2961.2
## <none> 160519 2961.8
## - speed 1 2544 163063 2963.4
## - steel 1 2637 163156 2963.7
## - water 1 2764 163283 2964.1
## - spattack 1 4525 165044 2969.4
## - normal 1 6106 166626 2974.2
## - spdefense 1 14816 175335 2999.6
## - attack 1 35013 195533 3054.0
##
## Step: AIC=2958.06
## hp ~ attack + spattack + spdefense + speed + flying + ghost +
## ground + ice + normal + steel + water
##
## Df Sum of Sq RSS AIC
## - flying 1 1387 162712 2956.1
## - ghost 1 1636 162961 2956.9
## - ice 1 1644 162969 2956.9
## - ground 1 1796 163121 2957.4
## <none> 161325 2958.1
## - speed 1 2170 163495 2958.5
## - water 1 2610 163935 2959.8
## - steel 1 2847 164172 2960.6
## - spattack 1 5028 166353 2967.2
## - normal 1 6592 167916 2971.8
## - spdefense 1 14517 175842 2994.8
## - attack 1 34211 195535 3047.8
##
## Step: AIC=2956.12
## hp ~ attack + spattack + spdefense + speed + ghost + ground +
## ice + normal + steel + water
##
## Df Sum of Sq RSS AIC
## - ice 1 1500 164212 2954.5
## - speed 1 1562 164274 2954.7
## - ground 1 1677 164389 2955.0
## - ghost 1 1784 164496 2955.3
## <none> 162712 2956.1
## - water 1 2323 165036 2957.0
## - steel 1 3053 165765 2959.2
## - spattack 1 4964 167676 2964.9
## - normal 1 6764 169476 2970.2
## - spdefense 1 14391 177103 2992.2
## - attack 1 33713 196426 3043.9
##
## Step: AIC=2954.48
## hp ~ attack + spattack + spdefense + speed + ghost + ground +
## normal + steel + water
##
## Df Sum of Sq RSS AIC
## - speed 1 1618 165831 2953.2
## - ground 1 1673 165885 2953.3
## - ghost 1 1851 166063 2953.9
## <none> 164212 2954.5
## - water 1 2242 166454 2955.0
## - steel 1 3427 167639 2958.6
## - spattack 1 5046 169258 2963.4
## - normal 1 6263 170475 2966.9
## - spdefense 1 14593 178805 2990.8
## - attack 1 34373 198586 3043.1
##
## Step: AIC=2953.17
## hp ~ attack + spattack + spdefense + ghost + ground + normal +
## steel + water
##
## Df Sum of Sq RSS AIC
## - ghost 1 1555 167386 2951.6
## - ground 1 1921 167752 2952.7
## <none> 165831 2953.2
## - water 1 2485 168315 2954.4
## - steel 1 2803 168634 2955.3
## - spattack 1 3735 169566 2958.1
## - normal 1 5510 171341 2963.3
## - spdefense 1 14037 179868 2987.5
## - attack 1 32757 198588 3036.9
##
## Step: AIC=2951.61
## hp ~ attack + spattack + spdefense + ground + normal + steel +
## water
##
## Df Sum of Sq RSS AIC
## <none> 167386 2951.6
## - ground 1 2134 169520 2951.7
## - water 1 2987 170373 2954.2
## - steel 1 3152 170538 2954.7
## - spattack 1 3554 170940 2955.9
## - normal 1 6080 173466 2963.2
## - spdefense 1 13948 181334 2985.3
## - attack 1 33522 200908 3036.5
summary(mbic)
##
## Call:
## lm(formula = hp ~ attack + spattack + spdefense + ground + normal +
## steel + water, data = data[-which(t == 231), ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -46.271 -10.977 -2.112 8.264 144.950
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.35734 2.92848 6.269 7.99e-10 ***
## attack 0.28805 0.02905 9.916 < 2e-16 ***
## spattack 0.10706 0.03316 3.229 0.00133 **
## spdefense 0.23542 0.03680 6.396 3.71e-10 ***
## groundTRUE 7.72983 3.08949 2.502 0.01267 *
## normalTRUE 11.50007 2.72321 4.223 2.87e-05 ***
## steelTRUE -10.69788 3.51821 -3.041 0.00249 **
## waterTRUE 6.65625 2.24886 2.960 0.00323 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.46 on 491 degrees of freedom
## Multiple R-squared: 0.4064, Adjusted R-squared: 0.398
## F-statistic: 48.03 on 7 and 491 DF, p-value: < 2.2e-16
outlierTest(mbic)
## rstudent unadjusted p-value Bonferonni p
## 218 8.431894 3.8291e-16 1.9107e-13
## 352 5.558996 4.4638e-08 2.2274e-05
plot(mbic)
influencePlot(mbic)
## StudRes Hat CookD
## 751 -1.0471733 0.064736284 0.0094858316
## 352 5.5589963 0.016334337 0.0604619144
## 752 -0.1524967 0.063402813 0.0001971749
## 218 8.4318944 0.009387304 0.0736955055
ncvTest(mbic)
## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 0.06875731, Df = 1, p = 0.79315
vif(mbic)
## attack spattack spdefense ground normal steel water
## 1.257610 1.599520 1.454313 1.076962 1.081476 1.055632 1.046175
mfinal = lm(hp ~ attack + spattack + spdefense + ground + normal + steel + water, data = test)
summary(mfinal)
##
## Call:
## lm(formula = hp ~ attack + spattack + spdefense + ground + normal +
## steel + water, data = test)
##
## Residuals:
## Min 1Q Median 3Q Max
## -51.731 -12.355 -3.645 6.510 169.453
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.68413 5.13633 4.806 2.47e-06 ***
## attack 0.16280 0.04880 3.336 0.00096 ***
## spattack 0.11692 0.05361 2.181 0.02999 *
## spdefense 0.29357 0.06153 4.771 2.89e-06 ***
## groundTRUE 9.57931 5.33305 1.796 0.07349 .
## normalTRUE 20.13220 4.16540 4.833 2.17e-06 ***
## steelTRUE -3.96829 6.18219 -0.642 0.52145
## waterTRUE 2.32774 4.25522 0.547 0.58477
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 24.59 on 292 degrees of freedom
## Multiple R-squared: 0.2492, Adjusted R-squared: 0.2312
## F-statistic: 13.85 on 7 and 292 DF, p-value: 1.738e-15
outlierTest(mfinal)
## rstudent unadjusted p-value Bonferonni p
## 122 7.761370 1.4350e-13 4.3050e-11
## 262 7.326360 2.3386e-12 7.0157e-10
## 656 4.609078 6.0605e-06 1.8182e-03
plot(mfinal)
influencePlot(mfinal)
## StudRes Hat CookD
## 416 -0.9950667 0.09868741 0.01355237
## 430 -1.3350373 0.11142279 0.02786209
## 122 7.7613696 0.05171101 0.34135744
## 262 7.3263596 0.06710540 0.40886860
mfull3 = lm(hp ~ attack + defense + spattack + spdefense + speed + generation + legendary + bug + dark + dragon + electric + fairy + fighting + fire + flying + ghost + grass + ground + ice + normal + poison + psychic + rock + steel + water + normal*flying + bug*flying, data = data[data$dex != 213 & data$hp <= mean(data$hp)+sd(data$hp)*2.5,])
summary(mfull3)
##
## Call:
## lm(formula = hp ~ attack + defense + spattack + spdefense + speed +
## generation + legendary + bug + dark + dragon + electric +
## fairy + fighting + fire + flying + ghost + grass + ground +
## ice + normal + poison + psychic + rock + steel + water +
## normal * flying + bug * flying, data = data[data$dex != 213 &
## data$hp <= mean(data$hp) + sd(data$hp) * 2.5, ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -46.963 -9.171 -1.697 8.422 60.607
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.78731 3.68505 3.470 0.000569 ***
## attack 0.25799 0.03044 8.476 3.20e-16 ***
## defense 0.09562 0.03432 2.786 0.005562 **
## spattack 0.14923 0.03300 4.522 7.80e-06 ***
## spdefense 0.18192 0.03496 5.203 2.95e-07 ***
## speed -0.05782 0.03121 -1.853 0.064586 .
## generation2 7.49312 2.44197 3.068 0.002279 **
## generation3 2.40005 2.18889 1.096 0.273447
## generation4 8.15462 2.42684 3.360 0.000844 ***
## generation5 8.57697 2.19053 3.915 0.000104 ***
## generation6 7.66835 2.77589 2.762 0.005967 **
## legendaryTrue 1.42109 2.95380 0.481 0.630670
## bugTRUE -0.16689 3.08695 -0.054 0.956907
## darkTRUE -3.03808 2.84375 -1.068 0.285930
## dragonTRUE -0.72945 3.18401 -0.229 0.818896
## electricTRUE -1.39601 3.43036 -0.407 0.684230
## fairyTRUE 1.08070 3.49637 0.309 0.757392
## fightingTRUE 1.27905 3.07253 0.416 0.677396
## fireTRUE -3.36886 3.21086 -1.049 0.294635
## flyingTRUE 7.49769 2.58585 2.900 0.003917 **
## ghostTRUE -12.45051 3.59144 -3.467 0.000576 ***
## grassTRUE -1.14230 2.59394 -0.440 0.659874
## groundTRUE 8.52792 2.72143 3.134 0.001837 **
## iceTRUE 5.92305 3.26748 1.813 0.070526 .
## normalTRUE 11.36375 3.10225 3.663 0.000278 ***
## poisonTRUE 5.73867 2.85734 2.008 0.045187 *
## psychicTRUE -2.09688 2.98480 -0.703 0.482712
## rockTRUE -5.45689 2.89390 -1.886 0.059973 .
## steelTRUE -12.17275 3.28952 -3.700 0.000241 ***
## waterTRUE 3.70532 2.41138 1.537 0.125080
## flyingTRUE:normalTRUE -7.25462 5.46106 -1.328 0.184697
## bugTRUE:flyingTRUE -4.87279 6.04304 -0.806 0.420460
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.78 on 459 degrees of freedom
## Multiple R-squared: 0.558, Adjusted R-squared: 0.5282
## F-statistic: 18.69 on 31 and 459 DF, p-value: < 2.2e-16
outlierTest(mfull3)
## rstudent unadjusted p-value Bonferonni p
## 186 4.323786 1.8834e-05 0.0092475
plot(mfull3)
influencePlot(mfull3)
## StudRes Hat CookD
## 751 -0.5361895 0.14694464 0.001550022
## 796 -3.4375772 0.12527684 0.051670077
## 138 -1.5902203 0.14372799 0.013220568
## 489 3.8057344 0.06517372 0.030654518
## 186 4.3237859 0.06569400 0.039553686
mbic2 = stepAIC(mfull3, k = log(length(mfull3$residuals)))
## Start: AIC=2809.89
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + dragon + electric + fairy + fighting +
## fire + flying + ghost + grass + ground + ice + normal + poison +
## psychic + rock + steel + water + normal * flying + bug *
## flying
##
## Df Sum of Sq RSS AIC
## - dragon 1 11.5 100258 2803.8
## - fairy 1 20.9 100267 2803.8
## - electric 1 36.2 100282 2803.9
## - fighting 1 37.8 100284 2803.9
## - grass 1 42.4 100289 2803.9
## - legendary 1 50.6 100297 2803.9
## - psychic 1 107.8 100354 2804.2
## - bug:flying 1 142.0 100388 2804.4
## - generation 5 5366.1 105612 2804.5
## - fire 1 240.4 100487 2804.9
## - dark 1 249.3 100496 2804.9
## - flying:normal 1 385.4 100632 2805.6
## - water 1 515.7 100762 2806.2
## - ice 1 717.7 100964 2807.2
## - speed 1 749.6 100996 2807.3
## - rock 1 776.6 101023 2807.5
## - poison 1 881.0 101127 2808.0
## <none> 100246 2809.9
## - defense 1 1694.9 101941 2811.9
## - ground 1 2144.6 102391 2814.1
## - ghost 1 2624.8 102871 2816.4
## - steel 1 2990.7 103237 2818.1
## - spattack 1 4466.3 104713 2825.1
## - spdefense 1 5913.4 106160 2831.8
## - attack 1 15690.5 115937 2875.1
##
## Step: AIC=2803.75
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + electric + fairy + fighting + fire +
## flying + ghost + grass + ground + ice + normal + poison +
## psychic + rock + steel + water + flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - fairy 1 27.5 100285 2797.7
## - electric 1 28.8 100287 2797.7
## - grass 1 32.8 100291 2797.7
## - legendary 1 50.1 100308 2797.8
## - fighting 1 53.8 100312 2797.8
## - psychic 1 96.4 100354 2798.0
## - bug:flying 1 137.7 100396 2798.2
## - generation 5 5354.9 105613 2798.3
## - fire 1 230.1 100488 2798.7
## - dark 1 237.9 100496 2798.7
## - flying:normal 1 387.1 100645 2799.4
## - water 1 638.3 100896 2800.7
## - speed 1 749.8 101008 2801.2
## - rock 1 772.2 101030 2801.3
## - ice 1 793.7 101051 2801.4
## - poison 1 963.8 101222 2802.2
## <none> 100258 2803.8
## - defense 1 1686.5 101944 2805.7
## - ground 1 2247.8 102506 2808.4
## - ghost 1 2685.1 102943 2810.5
## - steel 1 3026.8 103285 2812.2
## - spattack 1 4477.8 104736 2819.0
## - spdefense 1 5902.9 106161 2825.6
## - attack 1 15712.6 115970 2869.0
##
## Step: AIC=2797.68
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + electric + fighting + fire + flying +
## ghost + grass + ground + ice + normal + poison + psychic +
## rock + steel + water + flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - fighting 1 43.5 100329 2791.7
## - electric 1 45.4 100331 2791.7
## - legendary 1 47.8 100333 2791.7
## - grass 1 48.1 100333 2791.7
## - psychic 1 122.5 100408 2792.1
## - bug:flying 1 140.0 100425 2792.2
## - generation 5 5370.9 105656 2792.3
## - dark 1 270.1 100555 2792.8
## - fire 1 278.0 100563 2792.8
## - flying:normal 1 382.2 100668 2793.4
## - water 1 611.3 100897 2794.5
## - ice 1 766.1 101051 2795.2
## - speed 1 771.1 101056 2795.2
## - rock 1 825.0 101110 2795.5
## - poison 1 936.4 101222 2796.1
## <none> 100285 2797.7
## - defense 1 1678.3 101964 2799.6
## - ground 1 2223.5 102509 2802.3
## - ghost 1 2884.7 103170 2805.4
## - steel 1 3045.1 103330 2806.2
## - spattack 1 4553.3 104839 2813.3
## - spdefense 1 6093.3 106379 2820.4
## - attack 1 15832.5 116118 2863.5
##
## Step: AIC=2791.7
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## legendary + bug + dark + electric + fire + flying + ghost +
## grass + ground + ice + normal + poison + psychic + rock +
## steel + water + flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - legendary 1 42.9 100372 2785.7
## - electric 1 62.3 100391 2785.8
## - grass 1 65.4 100394 2785.8
## - bug:flying 1 131.9 100461 2786.2
## - psychic 1 139.8 100469 2786.2
## - generation 5 5428.4 105757 2786.6
## - fire 1 297.5 100626 2787.0
## - dark 1 323.6 100652 2787.1
## - flying:normal 1 368.1 100697 2787.3
## - water 1 570.9 100900 2788.3
## - ice 1 724.5 101053 2789.0
## - speed 1 752.1 101081 2789.2
## - poison 1 900.4 101229 2789.9
## - rock 1 904.5 101233 2789.9
## <none> 100329 2791.7
## - defense 1 1659.4 101988 2793.6
## - ground 1 2200.5 102529 2796.2
## - ghost 1 3022.4 103351 2800.1
## - steel 1 3178.7 103508 2800.8
## - spattack 1 4529.4 104858 2807.2
## - spdefense 1 6147.3 106476 2814.7
## - attack 1 16901.8 117231 2861.9
##
## Step: AIC=2785.71
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## bug + dark + electric + fire + flying + ghost + grass + ground +
## ice + normal + poison + psychic + rock + steel + water +
## flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - electric 1 63.5 100435 2779.8
## - grass 1 69.2 100441 2779.9
## - psychic 1 136.4 100508 2780.2
## - bug:flying 1 152.1 100524 2780.3
## - fire 1 302.3 100674 2781.0
## - generation 5 5546.9 105919 2781.1
## - dark 1 345.4 100717 2781.2
## - flying:normal 1 392.2 100764 2781.4
## - water 1 553.1 100925 2782.2
## - ice 1 715.7 101087 2783.0
## - speed 1 737.2 101109 2783.1
## - poison 1 888.6 101260 2783.8
## - rock 1 919.1 101291 2784.0
## <none> 100372 2785.7
## - defense 1 1695.9 102068 2787.7
## - ground 1 2219.2 102591 2790.3
## - ghost 1 3060.0 103432 2794.3
## - steel 1 3271.9 103644 2795.3
## - spattack 1 4908.9 105281 2803.0
## - spdefense 1 6296.6 106668 2809.4
## - attack 1 17564.6 117936 2858.7
##
## Step: AIC=2779.83
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## bug + dark + fire + flying + ghost + grass + ground + ice +
## normal + poison + psychic + rock + steel + water + flying:normal +
## bug:flying
##
## Df Sum of Sq RSS AIC
## - grass 1 44.2 100479 2773.8
## - psychic 1 91.4 100527 2774.1
## - bug:flying 1 138.0 100573 2774.3
## - fire 1 252.8 100688 2774.9
## - dark 1 307.7 100743 2775.1
## - generation 5 5528.4 105964 2775.2
## - flying:normal 1 395.9 100831 2775.6
## - water 1 722.2 101157 2777.2
## - speed 1 772.4 101208 2777.4
## - ice 1 831.2 101266 2777.7
## - rock 1 875.7 101311 2777.9
## - poison 1 1034.9 101470 2778.7
## <none> 100435 2779.8
## - defense 1 1687.1 102122 2781.8
## - ground 1 2300.7 102736 2784.8
## - ghost 1 2996.6 103432 2788.1
## - steel 1 3243.9 103679 2789.2
## - spattack 1 4959.7 105395 2797.3
## - spdefense 1 6331.2 106766 2803.7
## - attack 1 18824.6 119260 2858.0
##
## Step: AIC=2773.85
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## bug + dark + fire + flying + ghost + ground + ice + normal +
## poison + psychic + rock + steel + water + flying:normal +
## bug:flying
##
## Df Sum of Sq RSS AIC
## - psychic 1 65.7 100545 2768.0
## - bug:flying 1 131.2 100611 2768.3
## - fire 1 220.0 100699 2768.7
## - generation 5 5497.5 105977 2769.0
## - dark 1 283.0 100762 2769.0
## - flying:normal 1 402.3 100882 2769.6
## - speed 1 744.5 101224 2771.3
## - rock 1 838.8 101318 2771.7
## - water 1 868.0 101347 2771.9
## - ice 1 899.3 101379 2772.0
## - poison 1 1046.9 101526 2772.7
## <none> 100479 2773.8
## - defense 1 1668.8 102148 2775.7
## - ground 1 2458.3 102938 2779.5
## - ghost 1 2954.6 103434 2781.9
## - steel 1 3214.7 103694 2783.1
## - spattack 1 4915.8 105395 2791.1
## - spdefense 1 6326.8 106806 2797.6
## - attack 1 19116.5 119596 2853.2
##
## Step: AIC=2767.97
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## bug + dark + fire + flying + ghost + ground + ice + normal +
## poison + rock + steel + water + flying:normal + bug:flying
##
## Df Sum of Sq RSS AIC
## - bug:flying 1 125.7 100671 2762.4
## - fire 1 181.8 100727 2762.7
## - dark 1 265.7 100811 2763.1
## - flying:normal 1 408.3 100954 2763.8
## - generation 5 5650.8 106196 2763.8
## - speed 1 785.3 101331 2765.6
## - rock 1 816.7 101362 2765.8
## - ice 1 977.1 101522 2766.5
## - water 1 1029.2 101574 2766.8
## - poison 1 1177.2 101722 2767.5
## <none> 100545 2768.0
## - defense 1 1661.6 102207 2769.8
## - ground 1 2485.0 103030 2773.8
## - ghost 1 2892.1 103437 2775.7
## - steel 1 3186.7 103732 2777.1
## - spattack 1 4898.8 105444 2785.1
## - spdefense 1 6261.3 106806 2791.4
## - attack 1 21057.6 121603 2855.1
##
## Step: AIC=2762.39
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## bug + dark + fire + flying + ghost + ground + ice + normal +
## poison + rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - bug 1 41.8 100713 2756.4
## - fire 1 169.6 100840 2757.0
## - dark 1 267.4 100938 2757.5
## - flying:normal 1 345.3 101016 2757.9
## - generation 5 5665.6 106337 2758.3
## - speed 1 746.8 101418 2759.8
## - rock 1 807.8 101479 2760.1
## - ice 1 980.0 101651 2760.9
## - water 1 1024.2 101695 2761.2
## - poison 1 1273.2 101944 2762.4
## <none> 100671 2762.4
## - defense 1 1683.7 102355 2764.3
## - ground 1 2477.3 103148 2768.1
## - ghost 1 2917.5 103588 2770.2
## - steel 1 3121.1 103792 2771.2
## - spattack 1 4794.1 105465 2779.0
## - spdefense 1 6255.6 106927 2785.8
## - attack 1 21128.9 121800 2849.7
##
## Step: AIC=2756.4
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## dark + fire + flying + ghost + ground + ice + normal + poison +
## rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - fire 1 156.5 100869 2751.0
## - dark 1 247.4 100960 2751.4
## - flying:normal 1 335.8 101049 2751.8
## - generation 5 5633.2 106346 2752.1
## - speed 1 754.0 101467 2753.9
## - rock 1 788.8 101502 2754.0
## - ice 1 1025.8 101738 2755.2
## - water 1 1125.2 101838 2755.7
## - poison 1 1245.7 101958 2756.2
## <none> 100713 2756.4
## - defense 1 1664.7 102377 2758.2
## - ground 1 2584.4 103297 2762.6
## - ghost 1 2877.3 103590 2764.0
## - steel 1 3143.6 103856 2765.3
## - spattack 1 4971.8 105685 2773.9
## - spdefense 1 6366.2 107079 2780.3
## - attack 1 21109.6 121822 2843.6
##
## Step: AIC=2750.96
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## dark + flying + ghost + ground + ice + normal + poison +
## rock + steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - dark 1 234.5 101104 2745.9
## - generation 5 5548.5 106418 2746.3
## - flying:normal 1 337.4 101207 2746.4
## - speed 1 761.5 101631 2748.5
## - rock 1 765.3 101635 2748.5
## - ice 1 1132.3 102001 2750.2
## - water 1 1280.2 102149 2751.0
## <none> 100869 2751.0
## - poison 1 1358.2 102227 2751.3
## - defense 1 1655.2 102524 2752.8
## - ground 1 2611.2 103480 2757.3
## - ghost 1 2860.1 103729 2758.5
## - steel 1 3057.4 103927 2759.4
## - spattack 1 4818.4 105688 2767.7
## - spdefense 1 6558.9 107428 2775.7
## - attack 1 21097.5 121967 2838.0
##
## Step: AIC=2745.91
## hp ~ attack + defense + spattack + spdefense + speed + generation +
## flying + ghost + ground + ice + normal + poison + rock +
## steel + water + flying:normal
##
## Df Sum of Sq RSS AIC
## - generation 5 5395.9 106500 2740.4
## - flying:normal 1 351.0 101455 2741.4
## - rock 1 718.4 101822 2743.2
## - speed 1 797.5 101901 2743.6
## - ice 1 1189.5 102293 2745.4
## <none> 101104 2745.9
## - water 1 1319.6 102423 2746.1
## - poison 1 1423.8 102528 2746.6
## - defense 1 1725.5 102829 2748.0
## - ground 1 2713.8 103817 2752.7
## - ghost 1 2941.4 104045 2753.8
## - steel 1 2955.9 104060 2753.9
## - spattack 1 4937.8 106041 2763.1
## - spdefense 1 6591.5 107695 2770.7
## - attack 1 21004.1 122108 2832.4
##
## Step: AIC=2740.45
## hp ~ attack + defense + spattack + spdefense + speed + flying +
## ghost + ground + ice + normal + poison + rock + steel + water +
## flying:normal
##
## Df Sum of Sq RSS AIC
## - flying:normal 1 526.1 107026 2736.7
## - poison 1 533.0 107033 2736.7
## - rock 1 730.0 107230 2737.6
## - water 1 776.8 107276 2737.8
## - speed 1 956.6 107456 2738.7
## <none> 106500 2740.4
## - defense 1 1471.9 107971 2741.0
## - ice 1 1538.7 108038 2741.3
## - ground 1 2435.5 108935 2745.4
## - steel 1 2568.9 109069 2746.0
## - ghost 1 2948.3 109448 2747.7
## - spattack 1 4818.3 111318 2756.0
## - spdefense 1 7356.4 113856 2767.1
## - attack 1 22228.1 128728 2827.3
##
## Step: AIC=2736.68
## hp ~ attack + defense + spattack + spdefense + speed + flying +
## ghost + ground + ice + normal + poison + rock + steel + water
##
## Df Sum of Sq RSS AIC
## - poison 1 500.1 107526 2732.8
## - water 1 732.4 107758 2733.8
## - rock 1 749.7 107775 2733.9
## - speed 1 928.2 107954 2734.7
## <none> 107026 2736.7
## - defense 1 1467.7 108493 2737.2
## - ice 1 1491.0 108517 2737.3
## - flying 1 2002.5 109028 2739.6
## - ground 1 2411.4 109437 2741.4
## - steel 1 2663.2 109689 2742.6
## - ghost 1 3013.0 110039 2744.1
## - spattack 1 4718.1 111744 2751.7
## - normal 1 5017.0 112043 2753.0
## - spdefense 1 7693.9 114720 2764.6
## - attack 1 22151.9 129178 2822.8
##
## Step: AIC=2732.77
## hp ~ attack + defense + spattack + spdefense + speed + flying +
## ghost + ground + ice + normal + rock + steel + water
##
## Df Sum of Sq RSS AIC
## - water 1 608.5 108134 2729.3
## - rock 1 870.9 108397 2730.5
## - speed 1 950.1 108476 2730.9
## - ice 1 1335.7 108861 2732.6
## <none> 107526 2732.8
## - defense 1 1446.5 108972 2733.1
## - flying 1 1878.1 109404 2735.1
## - ground 1 2228.8 109755 2736.7
## - steel 1 2923.4 110449 2739.7
## - ghost 1 3004.9 110531 2740.1
## - spattack 1 4561.5 112087 2747.0
## - normal 1 4632.6 112158 2747.3
## - spdefense 1 7676.9 115203 2760.4
## - attack 1 21977.8 129504 2817.9
##
## Step: AIC=2729.34
## hp ~ attack + defense + spattack + spdefense + speed + flying +
## ghost + ground + ice + normal + rock + steel
##
## Df Sum of Sq RSS AIC
## - rock 1 856.8 108991 2727.0
## - speed 1 955.2 109090 2727.5
## - ice 1 1267.6 109402 2728.9
## <none> 108134 2729.3
## - flying 1 1721.9 109856 2730.9
## - defense 1 1784.9 109919 2731.2
## - ground 1 2097.0 110231 2732.6
## - ghost 1 3386.9 111521 2738.3
## - steel 1 3425.7 111560 2738.5
## - normal 1 4236.7 112371 2742.0
## - spattack 1 4813.3 112948 2744.5
## - spdefense 1 7305.1 115439 2755.2
## - attack 1 21502.7 129637 2812.2
##
## Step: AIC=2727.02
## hp ~ attack + defense + spattack + spdefense + speed + flying +
## ghost + ground + ice + normal + steel
##
## Df Sum of Sq RSS AIC
## - speed 1 779.2 109770 2724.3
## - defense 1 1213.8 110205 2726.3
## - ice 1 1374.1 110365 2727.0
## <none> 108991 2727.0
## - flying 1 1716.7 110708 2728.5
## - ground 1 2139.6 111131 2730.4
## - ghost 1 3084.0 112075 2734.5
## - steel 1 3265.1 112256 2735.3
## - normal 1 4583.3 113574 2741.1
## - spattack 1 5280.4 114272 2744.1
## - spdefense 1 7913.6 116905 2755.2
## - attack 1 21360.9 130352 2808.7
##
## Step: AIC=2724.32
## hp ~ attack + defense + spattack + spdefense + flying + ghost +
## ground + ice + normal + steel
##
## Df Sum of Sq RSS AIC
## - flying 1 1319.8 111090 2724.0
## - ice 1 1382.7 111153 2724.3
## <none> 109770 2724.3
## - defense 1 1658.6 111429 2725.5
## - ground 1 2261.0 112031 2728.1
## - ghost 1 2863.4 112634 2730.8
## - steel 1 3063.7 112834 2731.6
## - normal 1 4164.3 113935 2736.4
## - spattack 1 4533.8 114304 2738.0
## - spdefense 1 7360.6 117131 2750.0
## - attack 1 20776.9 130547 2803.2
##
## Step: AIC=2724
## hp ~ attack + defense + spattack + spdefense + ghost + ground +
## ice + normal + steel
##
## Df Sum of Sq RSS AIC
## - ice 1 1255.2 112345 2723.3
## <none> 111090 2724.0
## - defense 1 1549.7 112640 2724.6
## - ground 1 2105.0 113195 2727.0
## - ghost 1 3076.1 114166 2731.2
## - steel 1 3307.8 114398 2732.2
## - normal 1 4549.9 115640 2737.5
## - spattack 1 4813.5 115904 2738.6
## - spdefense 1 7485.7 118576 2749.8
## - attack 1 21104.1 132194 2803.2
##
## Step: AIC=2723.32
## hp ~ attack + defense + spattack + spdefense + ghost + ground +
## normal + steel
##
## Df Sum of Sq RSS AIC
## <none> 112345 2723.3
## - defense 1 1526.2 113872 2723.8
## - ground 1 2116.3 114462 2726.3
## - ghost 1 3121.2 115466 2730.6
## - steel 1 3606.4 115952 2732.6
## - normal 1 4177.0 116522 2735.0
## - spattack 1 4862.3 117208 2737.9
## - spdefense 1 7586.9 119932 2749.2
## - attack 1 21553.5 133899 2803.3
summary(mbic2)
##
## Call:
## lm(formula = hp ~ attack + defense + spattack + spdefense + ghost +
## ground + normal + steel, data = data[data$dex != 213 & data$hp <=
## mean(data$hp) + sd(data$hp) * 2.5, ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -46.814 -9.655 -1.544 8.564 63.819
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 17.34339 2.49922 6.940 1.27e-11 ***
## attack 0.25289 0.02630 9.616 < 2e-16 ***
## defense 0.08269 0.03231 2.559 0.010804 *
## spattack 0.12656 0.02771 4.567 6.28e-06 ***
## spdefense 0.19415 0.03403 5.705 2.03e-08 ***
## ghostTRUE -12.07666 3.30021 -3.659 0.000281 ***
## groundTRUE 7.74515 2.57034 3.013 0.002720 **
## normalTRUE 9.61770 2.27191 4.233 2.76e-05 ***
## steelTRUE -12.23566 3.11062 -3.934 9.60e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.27 on 482 degrees of freedom
## Multiple R-squared: 0.5047, Adjusted R-squared: 0.4964
## F-statistic: 61.39 on 8 and 482 DF, p-value: < 2.2e-16
outlierTest(mbic2)
## rstudent unadjusted p-value Bonferonni p
## 186 4.263101 2.4274e-05 0.011918
plot(mbic2)
influencePlot(mbic2)
## StudRes Hat CookD
## 751 -0.2643268 0.119429091 0.001054932
## 489 3.8515213 0.038678628 0.064466652
## 752 0.4462974 0.099566112 0.002451253
## 186 4.2631006 0.004254635 0.008331394
## 473 3.6142046 0.049254624 0.073355201
ncvTest(mbic2)
## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 1.110854, Df = 1, p = 0.2919
vif(mbic2)
## attack defense spattack spdefense ghost ground normal
## 1.479233 1.888897 1.615273 1.789073 1.024396 1.088649 1.064312
## steel
## 1.205654
mfinal2 = lm(hp ~ attack + defense + spattack + spdefense + ghost + ground + normal + steel, data = test[test$hp <= mean(data$hp)+sd(data$hp)*2.5,])
summary(mfinal2)
##
## Call:
## lm(formula = hp ~ attack + defense + spattack + spdefense + ghost +
## ground + normal + steel, data = test[test$hp <= mean(data$hp) +
## sd(data$hp) * 2.5, ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -53.615 -9.256 -2.061 6.390 59.358
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 25.74911 3.46339 7.435 1.25e-12 ***
## attack 0.19425 0.03549 5.474 9.72e-08 ***
## defense 0.07101 0.04099 1.732 0.08431 .
## spattack 0.14975 0.03707 4.040 6.88e-05 ***
## spdefense 0.13650 0.04916 2.777 0.00586 **
## ghostTRUE -7.62474 3.87030 -1.970 0.04981 *
## groundTRUE 7.97582 3.68522 2.164 0.03128 *
## normalTRUE 9.58041 2.89738 3.307 0.00107 **
## steelTRUE -4.99902 4.34311 -1.151 0.25069
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.46 on 283 degrees of freedom
## Multiple R-squared: 0.3988, Adjusted R-squared: 0.3818
## F-statistic: 23.46 on 8 and 283 DF, p-value: < 2.2e-16
outlierTest(mfinal2)
## No Studentized residuals with Bonferonni p < 0.05
## Largest |rstudent|:
## rstudent unadjusted p-value Bonferonni p
## 45 3.752167 0.00021282 0.062144
plot(mfinal2)
influencePlot(mfinal2)
## StudRes Hat CookD
## 430 -2.7482358 0.12536276 0.11756139
## 45 3.7521668 0.03338286 0.05163806
## 797 -3.3781552 0.03584554 0.04546884
## 590 2.2619737 0.13221175 0.08537233
## 334 -0.9251977 0.13296255 0.01459282